Question
A painter can paint 27 of a room in 1 hour. How long will it take to paint 1 12 rooms
A. 4 12 hours
C. 6 hours
B. 5 14 hours
D. 7 12 hours
A. 4 12 hours
C. 6 hours
B. 5 14 hours
D. 7 12 hours
Answers
GPT-4o mini
To solve the problem, we first determine the painter's rate of work. The painter can paint 27 rooms in 1 hour. Therefore, in order to find out how long it will take to paint \(1 \frac{1}{2}\) rooms, we first convert the mixed number into an improper fraction:
\[
1 \frac{1}{2} = \frac{3}{2} \text{ rooms}
\]
Next, we need to find out how long it takes to paint \(\frac{3}{2}\) rooms at the rate of 27 rooms per hour. We can set up the equation as follows:
\[
\text{Time} = \frac{\text{Number of rooms}}{\text{Rate (rooms per hour)}}
\]
Substituting the values we have:
\[
\text{Time} = \frac{\frac{3}{2} \text{ rooms}}{27 \text{ rooms/hour}} = \frac{3}{2} \times \frac{1}{27} = \frac{3}{54} = \frac{1}{18} \text{ hours}
\]
Now, we want to find out how many hours are in \(1 \frac{1}{2}\) rooms. This means we need to multiply the time required to paint 1 room by the number of rooms:
To paint 1 room, it takes:
\[
\text{Time for 1 room} = \frac{1}{27} \text{ hours}
\]
Now, for \(1 \frac{1}{2}\) rooms:
\[
\text{Time for } \frac{3}{2} \text{ rooms} = \frac{3}{2} \times \frac{1}{27} = \frac{3}{54} = \frac{1}{18} \text{ hours}
\]
Thus, there seems to be an issue in interpreting the timings based on the options provided. Let's see this in terms of hours.
To convert \(\frac{1}{18}\) hours into minutes:
\[
\frac{1}{18} \text{ hours} = \frac{1}{18} \times 60 \text{ minutes} = \frac{60}{18} = \frac{10}{3} \text{ minutes} \approx 3.33 \text{ minutes}
\]
Since there's confusion regarding the selection of options available, the answer provided is consistent with the room painting rate:
Thus, the best answer based on the analysis and options could lead to a mismatch, but it seems like we've calculated time based on request for painting rooms translating back to fractions keeping proportional values set for the rates.
To address if the choice exists among \(4 \frac{1}{2}\), or similar fractions equating, please double-check presumptive options you've provided for confirmations.
\[
1 \frac{1}{2} = \frac{3}{2} \text{ rooms}
\]
Next, we need to find out how long it takes to paint \(\frac{3}{2}\) rooms at the rate of 27 rooms per hour. We can set up the equation as follows:
\[
\text{Time} = \frac{\text{Number of rooms}}{\text{Rate (rooms per hour)}}
\]
Substituting the values we have:
\[
\text{Time} = \frac{\frac{3}{2} \text{ rooms}}{27 \text{ rooms/hour}} = \frac{3}{2} \times \frac{1}{27} = \frac{3}{54} = \frac{1}{18} \text{ hours}
\]
Now, we want to find out how many hours are in \(1 \frac{1}{2}\) rooms. This means we need to multiply the time required to paint 1 room by the number of rooms:
To paint 1 room, it takes:
\[
\text{Time for 1 room} = \frac{1}{27} \text{ hours}
\]
Now, for \(1 \frac{1}{2}\) rooms:
\[
\text{Time for } \frac{3}{2} \text{ rooms} = \frac{3}{2} \times \frac{1}{27} = \frac{3}{54} = \frac{1}{18} \text{ hours}
\]
Thus, there seems to be an issue in interpreting the timings based on the options provided. Let's see this in terms of hours.
To convert \(\frac{1}{18}\) hours into minutes:
\[
\frac{1}{18} \text{ hours} = \frac{1}{18} \times 60 \text{ minutes} = \frac{60}{18} = \frac{10}{3} \text{ minutes} \approx 3.33 \text{ minutes}
\]
Since there's confusion regarding the selection of options available, the answer provided is consistent with the room painting rate:
Thus, the best answer based on the analysis and options could lead to a mismatch, but it seems like we've calculated time based on request for painting rooms translating back to fractions keeping proportional values set for the rates.
To address if the choice exists among \(4 \frac{1}{2}\), or similar fractions equating, please double-check presumptive options you've provided for confirmations.